Experiencing anxiety when you travel is a problem for many. For specific anxieties such as this I find cognitive behavioural therapy useful, and you can speak to your GP about a referral. .
In addition to this I also recommend to practice mindfulness. Not only is this a technique that comes in useful in everyday life, but it can do a great deal to relieve anxiety whenever you are on public transport. -Do a breathing exercise to help you break the cycle of negative thoughts and take a look around you - observe the people, acknowledge your feelings for what they are.
To learn these techniques you can use an app like headspace or come and see a mindfulness trainer like myself.
Also to all my Londoners - TFL have an anxiety tunnel travel map. This map is an excellent resource for those wishing to avoid journeys where there are tunnels, serving as a great pre-journey planning aid and increasing access to public transport.